Rectangular concrete-filled double-skin steel tubular (CFDST) columns consisting of stainless-carbon steel tubes are high-performance composite columns that offer high corrosion resistance in harsh environments and have a wide range of applications in the construction industry. However, the buckling resistance of CFDST short and slender columns has not been properly investigated and design models for such columns need to be developed. In this paper, an extensive study on their performance is undertaken by employing the cost-effective fiber-based computation model. An accurate new confinement model for the confined concrete is suggested and implemented in the numerical modeling. The computational analysis procedures, which simulate the complete load-axial strain (−) curves, load-lateral deflection (−) curves, and interaction diagrams of CFDST columns, are presented. The experimental data available is employed to validate the numerical predictions. The fundamental behavior of CFDST columns is then studied to investigate the influences of a wide range of column parameters. On the setback of the lack of design specifications, design models for such columns are suggested and validated against the test and numerical results. The mathematical model developed is found to be a computationally efficient simulator that can simulate the responses of CFDST short and slender columns loaded either concentrically or eccentrically and the design models suggested can be used in the absence of the proper guidelines from the international design codes.